Use designParamEQ to
create parametric equalizers. You can design single-band parametric
equalizers or a cascade of parametric equalizers. Using a cascade
of parametric equalizers enables you to tune your frequency response
with precision.

Substituting the approximation for B into the
ΩB equation yields the
definition of α in [2]:

α=sin(ω0)sinh(ln22×ω0sinω0×BW)

Lowpass and Highpass Filter Design

Analog Low-Shelf Prototype

To design lowpass and highpass filters, Audio System
Toolbox uses a special case of the filter design for parametric
equalizers. In this design, the peak gain, G, is set to 0,
and GB2 is
set to 0.5 (–3 dB cutoff). The cutoff frequency of the lowpass filter
corresponds to 1 – ΩB. The cutoff
frequency of the highpass filter corresponds to
ΩB.

Digital Coefficients

The table summarizes the results of the bandpass bilinear transformation. The digital center
frequency, ω0, is set to
π for lowpass filters and 0 for highpass filters.

[4] Bristow-Johnson, Robert. "The Equivalence of Various Methods of
Computing Biquad Coefficients for Audio Parametric Equalizers." Presented at the
97th Convention of the AES, San Francisco, November 1994, AES Preprint
3906.